Explain why an even function does not have an inverse that is a function.

Question

and if log b < 0, what can you say about b?

Answer 1

recall that the inverse of a function results in a reflection in the line y = x

Any even function has a reflection in a vertical line, usually the y-axis
Thus its inverse would result in a reflection in a horizontal line.
Thus a vertical line test, (a test if the relation is a function) , would fail .